I've been working on the project "Using a Digital Camera to Measure Skyglow" and I've gotten stuck.I've completed the entire project, and really have no idea what to do with the information. I don't understand the purpose of taking the pictures of the blank paper, nor do I understand the importance of taking the picture at different f-stops. My digital camera is the Sony Cybershot with 10x optical zoom, and does not have the infinity feature on it. I don't know if that plays an important part in the project or not.Anyway, I've made all of my histograms, but do not understand them either. I don't know how looking at the histograms of the same stars at different f-stops would tell me how much light pollution there is. I've been reading all of the sites given to explain, but I still don't understand it.Somebody please help me! My project is due on January 18, and I don't know if I should start a completely new project or try to make do with the one I have.If you suggest I start a completely new project, please let me know which one I can do in that short amount of time and still get an okay grade on it. My projects always go into the Science Fair at my school as well (not that they win anything), so it needs to be presentable.

Please Please Please help me! Either help explain this Skyglow project, or help me find another easier project.

If you have completed the entire project and have data, then you should not think about changing experiments. You just need to write up your results for your display board. Here are some information that should help you complete your write up:

The purpose of this project is to measure the amount of background light in the night sky to determine what conditions would be best for skygazing. Your histograms should show a difference in the amount of gray in each photograph. The results with the highest amount of gray will be the highest level of skyglow, and results with the lowest amount will be best for skygazing.

The image processing program measures the average pixel intensity of each photograph and is the measurement that you need in order to compare results. Please answer the following questions?

Do your histograms show a number at the bottom? This is the pixel number Did you get reproducible results with the control photograph using indirect sunlight?Did you observe any difference in any of your sky photographs?Can you give me some examples of your data? Please upload a couple of histograms if you can.Please describe the different locations that you photographed.

Do you know what your independent and dependent variables are in this experiment?

Here is the information for doing a display board from the Science Buddies website:

Please let me know what you have written for the following sections so far: project title, research question, background information, materials list, procedure sections, and bibliography or literature cited.

Please answer as many questions as you can so I will understand what additional information you need to continue with this.

Thanks Donna. I apologize for not replying in a while. My Internet connection has been questionable, and we only just recently got it back into shape.

The imaging software I use is ImageJ, the one recommended, and so yes, I was able to create the histograms and see the pixel numbers.What exactly do you mean by reproducible results with the control? I took the control photos in indirect sunlight at the different shutter speeds (as it asks for), and as the time grew longer (1 second, 2 seconds, 4 seconds) each image grew lighter, and at shorter shutter speeds (1/250 seconds, 1/500 seconds, 1/1000 seconds) each image grew darker. When I put those into ImageJ, and created the histograms, they came out looking like this:(hopefully the images show up)

This first image is in the control group with shutter speed 1/8 of a second.The lighter color on the left side of the image is the actual picture I took.

My photos with the stars turned out the same way, with the ones exposed longer showing up with brighter spots of light, and the ones exposed for a shorter time were just completely black.Again, I don't understand your question "Do you see any difference in your sky photographs?"I did see differences, but that was only because I took the pictures at varying shutter speeds, so they came out either lighter or extremely dark.

Here are a few of my sky photographs:(again, in each of the photos, the left hand darker side is the actual image that the histogram is of)

I didn't actually take as much time as I would have liked to, to shoot pictures for this experiment, and I was only able to shoot picutes in one location (Riverside, CA).I'm not sure what my independent or dependent variables are....Thanks for the display board tip! That should help me a lot.

To answer your other questions about the project title, research question, background information (do you mean the research report?), materials list, procedure sections, and bibliography, I will try to upload those as a separate document in my next post.

These are the data results I came up with, along with the graphs.I don't know if the graphs are created correctly, but I went along with what I understood from the directions on the project on the science buddies website.

Thanks for all of the data and other information. You have done an impressive amount of work on this project, but I understand the problem you are having with the data analysis now; I thought it would be a matter of comparing the pixel numbers, but I’m not sure now. I am going to ask for help from one of the other experts for confirmation on the data analysis.

Please delete your personal e-mail address. We’re not allowed to communicate by personal e-mail, even though it would make sharing data a lot easier for your project. It’s an internet safety rule.

I will read the rest of your research paper and information for your display board and make some more detailed comments soon.

Wyvern, I hate to be the bearer of bad news, but despite the obvious amount of work you have done, I’m not sure you can finish this project in a meaningful way in the time remaining.

First, let me apologize for this project. In my opinion it is too advanced for a high-school student to undertake. Also the writeup is severely lacking on so many counts that it would be a challenge even for students with many more years of experience than you could possibly be expected to have. That this project is to blame for the situation you are now in is not going to be much consolation I’m sure. Second, I did not see Donna’s call for help until today because I have been (am) ill. But I don’t think that a more timely response would really have helped all that much.

There are two huge problems in what you have so far. First, the whole point of this project (not too clearly emphasized I fear) is to compare data taken at different sites. Data from one site does not permit comparisons to be made. This lack will be nearly impossible to remedy in the time remaining. Second, your images for the sky-glow measurements are severely under exposed; not enough photons were collected to see the very dim glow of the night sky (much fainter than is visible to the human eye). Had the exposures been long enough, I doubt you would even see the stars, as they would be totally saturated and contribute very little to the histograms (this is a good thing, since otherwise you would have had to remove all the data points around the brightest stars so as better to see the dim sky glow). Looking at your sample histograms I estimate you would need exposures at least ten times as long as your longest sky-glow exposure (80 rather than 8 sec). Why so long? It may be that the lens of your camera is too small (in technical jargon, the f-stop can not be set to as low a value as 2.8 — the recommended value), or the image detector (CCD) is less sensitive than that of the camera used in the example. Anyway, you need something like an average count of around 100, where the “control” (which should be called the “calibration”) shows that the camera has maximum dynamic range. To remedy this would require getting new images on cloud-free nights. That would need more time than it seems you have.

What is most critically missing from the on-line write-up (I don’t have easy access to back issues of Sky & Telescope) is an explanation of how to use the series of exposures on a white surface. These data are not really a control in the usual sense of that word. They give a calibration of your camera. In an ideal camera, the value of each pixel (PV) would be exactly proportional to how much light fell upon it over the course of the exposure, something like:

PV = k * S * T

where S is the number of photons/sec hitting the detector (unknown), T is the exposure time, and k is a constant set by the camera optics, the detector efficiency, the f-stop setting, and the focus distance.We know PV and T, thus

S = PV /( k * T)

For this ideal camera, one could measure the relative brightness of the diffuse sky glow from the value of any pixel (they would all be identical), for example to compare site A to site B using the same camera set up and the same exposure time T, we would have

(S at A)/(S at B) = [PV at A]/[PV at B]

and be able to get the relative brightness ratio for the two sites, without ever knowing the value of k, just that it is constant between the observations. That’s good, since k depends on lots of things in complicated ways.

What about a real, not ideal camera? For the real camera, each pixel will be a little different, so we use some measure of what all of them are doing — that is where the average and modes of the histograms of PV come in. I’ll just denote those as <PV> where the <> means average or mode. Worse, the actual PV observed will be distorted from the PV of the ideal camera,

<PV> = f[<PV> ideal]

Luckily, f[] depends on the product S*T rather than S or T alone. (As always, this s not exactly true, especially if the number of photons detected per second it very large; it is true enough for the cases of interest to us here.) We can exploit this observed feature to calibrate out the unknown function f.

where I have absorbed the unknown values of k and (S calibrator) into the definition of a new function g. This function g is just what you constructed from your “control” data. To use this calibration, we take an observed <PV> and find the corresponding exposure time on the control field that would have produced that value of <PV>. I’ll call that time the equivalent exposure time, EET. Formally we can “solve” to find EET by inverting the function g, EET = ginverse[PV]. That’s actually easy to do graphically. For a given value of <PV>, we move horizontally over to the curve you made of g[T], then drop down to find the equivalent exposure time EET that would have been needed in the cal setup to get the same count. Of course for this to work you need to make sky observations that are long enough to reach values of <PV> that are in the “nice” part of the curve g[]. From your plot that looks to be from 50 to 200 pixel val units.(Your exposures reached at most 8 for your longest exposure; that’s too low.) Suppose you had exposed for 80 seconds, then at your first site you would have seen something like <PV> ~80 (at best). Reading across from 80 on your calibration curve I get 0.02 seconds, which would be the value of EET for this site. Suppose you had data from a second site with all the same parameters, also at 80 seconds, and <P> was 120. Following the same procedure I (by eye — hard to do on log plots) yields an EET of 0.04. The ratio of the two EET values is then the ratio of the sky brightnesses of the two sites ( 0.04/0.02 = 2 ).

I see that you took a full set of exposure times at each site. I don’t think that was the intent (I hope not). Next time, if there is one, you only need a single exposure time (something like 10 times 8 seconds might work).

You may be curious about all the points on your sky curves at short exposures that yield the same value, <PV> around 0.5 What is happening is that you are seeing noise in the readout electronics of the CCD image detector. You would see the same thing if you blocked the aperture entirely. You can make your <PV> values more closely adhere to the S*T dependence the calibration technique requires if, as a first step, you subtract this low level from all your data before proceeding further with the other stages. As long as you are using exposures that produce <PV> much greater than 0.5, however, you can safely ignore this defect in the mathematical model of the exposure process.

John has helpfully provided the expert advice that we needed for this project and explained that you don't have enough data to actually measure skyglow. With this information, you can make a plan to finish your project on time. You actually have a complete project, however, you just didn't obtain the results that you expected. But your background research and results are valid and very worthwhile, and you should do very well at the science fair.

You don't have time to complete a set of measurements and multiple locations or switch to a different science project; you should just focus on writing up your project as it is.

You have completed all of the steps of a scientific investigation, and you can present all of the steps as they are including your results section. I will explain:

Here are the sections that you need to include on you display board from the Science Buddies website:

Title: "Measuring Skyglow." is a good title and will let the reader immediately know what the topic is.

Abstract: Your project is complicated, so you do need to include an abstract to let everyone know what happened in the project. You can wait and do your abstract last; it should be 2-3 sentences, very brief. One sentence to explain what you were doing and one sentence to say what happened.

Question: What is your research question? Is it something like, "does skyglow affect the brightness of stars," Or perhaps, "how does skyglow affect star brightness in your city?"

Hypothesis: Your hypothesis needs to be reworded. I believe that you meant to say something like you think that skyglow does affect star brightness.

Background: You have included a lot of information about astronomy in your research paper. For your display board, just use the last paragraph on skyglow. Go through it to see if you can shorten it and add one more sentence at the end to explain the purpose of your project. "In this project, I wanted to find out if________."

Materials: Add specific information on what equipment you used, the model of camera and computer, include the name of the software, the site where the software can be downloaded and what the software does; state the location of your experiment, or include a map with an "x" to show your general location."

Procedure: You should include a copy of your research paper and refer to it in the procedure section, but rewrite it to shorten it into a few steps. Remember shorter is better on a display board.

The Science Buddies procedure is written with general instructions your procedure section should be written with specific details that you did. For example, say: "The dynamic range of the specific brand and model of camera was measured using a piece of white paper illuminated by indirect in manual mode: sensitivty ISO200, aperture f/2.8, shutter speeds ranging from x to z."

Or, better yet, draw a series of pictures or make photographs and do a very short summary of the procedure so that the viewer can see what happened. For example, the first step would be a picture of a camera on a tripod focused on a piece of white paper and captioned. "The dynamic range of the camera was measured." Use arrows in between steps so the procedure looks like a flow chart and the viewer can see the sequence of steps.

Results: This is the most important part of your project, and what the science fair judges will be looking for. Include the data tables and the graphs if you have room. Make this section a large as possible and position it in the center of the board.

Conclusions: Alas, you did your project and obtained quantitative results, but you did not prove your hypothesis. So, in the first sentence, say that your did not prove your hypothesis. Then, explain what happened and what you would do next time to obtain the desired results. Use the equations and explanation that John provided to explain what happened. The main problem is that you did measure the pixels, but there was no reference point to compare the skyglow.

Literature cited: This should be in your research paper or in small print on the board. The science fair judges will want to know if you based your project on the scientific literature.

The idea was to study how the sky brightness changes as the observing conditions change. One experiment would be to see how the sky brightness depends on the time of day: brighter in the evening and pre-dawn hours, darker in the deep night. Another would be to see how the phase of the moon affects the sky brightness. Another would be to compare a completely clear night with a night with thin, nearly transparent cirrus clouds. Finally, one could compare the sky brightness at various locations where one might be considering building an observatory in order to find which has the darkest (best for astronomy) night sky, being careful to allow for the time of day and phase of the moon when making the comparisons. This last is the most common reason astronomers measure sky brightness.

Alright. Thank you very much John. I really appreciate you getting back to me so quickly.You and Donna have helped me so much. I don't think I would have been able to understand as much as I have without your help, so thank you for being so patient and explaining everything.